By a coincidence of history the Roman empire, at its start, has recently achieved a new geographical completeness. The campaigns of Pompey have led to the annexation of Syria in 64 BC and the capture of Jerusalem in 63. With Octavian's defeat of Cleopatra at Actium in 31 BC, Egypt too becomes a province. Just in time for the start of the empire, the eastern pieces of the jigsaw are in place.

The Mediterranean, centre of the known world (as its name states), has become what it will remain for the next four centuries - a Roman sea. And during the same period, until Constantine gives the city a new Christian role, the story of Rome itself becomes submerged in that of the wider Roman empire.

The rule of Augustus Caesar brings an unprecedented forty years of peace in Italy. With few setbacks on distant frontiers, Rome and its territories enjoy a steady increase in prosperity and trade.

The frontiers of empire are slightly extended. More important, they become stablized and properly defended. Professional careers are now possible in the army (recruits sign on for sixteen years, later increased to twenty) and in the civil service. Improved roads make it easier to keep in close touch with distant parts of the Roman world, and to move troops wherever they are needed. New towns, built to Roman design, are established in areas where there was previously no administrative structure.

The region in which Augustus makes the most effort to extend the empire is beyond the Alps into Germany. By 14 BC the German tribes are subdued up to the Danube. In the next five years Roman legions push forward to the Elbe. But this further border proves impossible to hold. In AD 9 Arminius, a German chieftain of great military skill, destroys three Roman legions in the Teutoburg Forest.

The Romans pull back (though they return briefly to avenge what seems a shameful defeat). The conclusion, bequeathed by Augustus to his successors, is that the Roman empire has some natural boundaries; to the north these are the Rhine and the Danube.

Within these boundaries the reign of Augustus introduces what becomes known as the Pax Romana, the Roman peace. For those within the empire this represents a real and unprecedented benefit.

Somehow, after the death of Augustus in AD 14, this fortunate state of affairs survives even the grotesque behaviour on the imperial throne of the descendants either of Augustus himself or of his second wife Livia. The family life of the Caesars, recorded in dramatic detail by Tacitus and others, has fascinated subsequent generations. But amazingly the empire not only survives this first dynasty of emperors (AD 14-68). It even grows.

The Julio-Claudian emperors: AD 14-68

The four successors of Augustus are known as the Julio-Claudian emperors because they descend either from Augustus (whose mother was a niece of Julius Caesar) or from his second wife, Livia, who is a member of the Claudii, another great Roman clan.

Augustus and Livia, married for fifty-two years, have no children of their own. The candidates for the succession are their children by previous marriages. After the death of three favoured heirs (probably from natural causes, though Roman gossip invariably suspects poison), the eventual successor is Tiberius, a son of Livia. On being acknowledged as the heir apparent, in AD 4, he becomes known as Tiberius Julius Caesar.

Tiberius: AD 14-37

Tiberius, inheriting in AD 14, continues the policies of Augustus. He keeps firm control of the army while showing due respect to the senate in Rome, and he behaves with personal modesty. He accords his predecessor divine status, but discourages any cult of himself as the living emperor. But in the later years of his life his behaviour brings him a different reputation.

For reasons which are not clear, he withdraws from Rome in AD 26 to live on the island of Capri. Ruling now as a remote figure (and decreeing the deaths of any who seem to challenge him, including several members of the imperial family), he comes to seem a monster. His death is welcomed in Rome. But his successor is worse.

Caligula: AD 37-41

By the time of Tiberius's death, in AD 37, Gaius Caesar is the only living male descendant of the emperor Augustus. His two elder brothers and his mother have been put to death in prison as a result of complex plots over the succession. Gaius Caesar himself is widely known by a nickname. As a small child, on campaign with his father against the Germans, he was often dressed in a miniature soldier's uniform. The soldiers called him Caligula, 'little boot', and the name has stuck.

It is probably the most charming thing about him.

Caligula's short reign is marked by wild extravagance and brutality. A serious illness in AD 37 leaves him more than a little mad (though it is not true that he makes his horse a consul). The result is the first of many occasions in which the army directly intervenes in the imperial succession. At an athletics contest in Rome, the Palatine games of AD 41, Caligula is murdered by a tribune of the Praetorian guard.

The next incident is one of the most famous in Roman imperial history. A soldier finds Caligula's supposedly pathetic uncle, Claudius, hiding in terror in the palace. He expects to be killed. Instead the praetorian guards force the senate to accept him as emperor.

Claudius: AD 41-54

A physical infirmity of some kind (it has been suggested that he may have had cerebral palsy) has caused the imperial family to consider Claudius a nonentity. He has busied himself with scholarly studies, writing books in Greek on such varied topics as the Etruscans and dice-playing. But when thrust into power, he proves a surprisingly effective emperor.

The empire is extended during his reign, with new provinces in northwest Africa (Mauretania), northern Greece (Thrace) and southern Britain. Claudius himself takes part in the British campaign, crossing the Thames and capturing what is now Colchester. He is so pleased with this achievement that he names his son Britannicus.

It is an understatement to say that Claudius's private life is dramatic. His promiscuous third wife, Messalina, the mother of Britannicus, plots against him with one of her lovers. He executes them in AD 48 and marries his niece, Agrippina. This is forbidden in Roman law, so he changes the law.

The niece, like everyone else in the family, has a scheme. Her son by a previous marriage is just three years older than Britannicus. She persuades Claudius to adopt this boy as his heir. With this agreed she poisons the old man, according to Roman gossip with toadstools. In AD 54 her 16-year-old son is proclaimed by the Praetorian guard as the emperor Nero.

Nero: AD 54-68

In the early years of Nero's reign he is guided by wise counsellors, particularly his old tutor Seneca. But soon he feels free to follow his own inclinations. Within a few years his riotous personal behaviour is deeply offending the Romans, who are also unimpressed by his insistence on performing in public - as charioteer, lute-player, poet and actor.

The murder in AD 55 of his young stepbrother Britannicus is hardly surprising in the context of the time; the boy is inevitably a threat as the son of the previous emperor. More unusual are the deaths of Nero's mother and wife.

In 58 Nero falls passionately in love with a married woman, Poppaea, the wife of Otho. Agrippina criticizes her son's liaison and is murdered in 59. Octavia, as his wife, is an unfortunate impediment; Nero divorces her, on a false charge of adultery, and then has her killed. He marries Poppaea in 62.

Nero becomes so unpopular that many believe he started the great Fire of Rome in 64, so as to give himself the grandiose pleasure of rebuilding the city. The accusation (which leads to the first persecution of the Christians) is unjust. So is the legend that the histrionic emperor plays his fiddle while Rome burns. But the stories reflect more genuine grievances.

Nero's extravagances have drained the imperial coffers. His inattention to affairs of state is reflected in serious rebellions at both extremes of the empire, in Britain in 60 and Palestine in 66. Soon even Romans are in revolt.

In AD 68 Roman officials and legions in Gaul and Spain declare themselves against the emperor. In Rome the praetorian guards follow suit. The senate passes a vote of censure on Nero. Recognizing the inevitable, he slits his throat.

There is no living male member of the Julian or Claudian families to claim the imperial crown. But the legions in various parts of the empire have their own ideas. For the first time it is realized, as Tacitus later writes, that emperors can be made elsewhere than in Rome. In the resulting clash of interests, AD 69 becomes the year of the four emperors.

Year of the four emperors: AD 69

Rebellion against Nero first comes to a head in Spain, where the governors of two neighbouring provinces have particular fears or grievances. One of them, Galba, believes that Nero is planning to assassinate him; the other, Otho, has lost his wife Poppaea to the emperor. In AD 68 Otho supports Galba in mounting a rebellion, but events run ahead of them. After Nero's suicide the senators adopt Galba as emperor. He takes the name Caesar and marches to Rome.

He then makes the serious tactical mistake of adopting someone other than Otho as his official heir. Otho suborns the Praetorian guard. Early in 69 Galba is assassinated in the forum. Otho is proclaimed emperor.

Meanwhile the army on the Rhine has a different idea, acclaiming its own commander, Vitellius. His forces move south, meeting and defeating those of Otho near Cremona in April. Otho commits suicide. In July Vitellius enters Rome as emperor.

But the soldiers in the east are equally reluctant to accept, unconsulted, the candidate of another section of the army. In July the legions at Alexandria acclaim Vespasian, now commanding the campaign to put down the Jewish revolt in Judaea. Their choice is rapidly endorsed by troops throughout the Middle East and then by the legions on the Danube - jealous opponents in this matter of their colleagues on the Rhine.

Vespasian's instinct is to bide his time, meanwhile perhaps withholding the important shipments of grain from Egypt to Rome, but his hand is forced by the Danube legions. They march south in his name, entering Rome in December. In a frenzy of destruction they murder many of the defenders, among them the emperor Vitellius. On December 21 the absent Vespasian is adopted by the senate, as the fourth emperor of the year.

The traumas of AD 69 remain a cautionary tale to succeeding generations. It is more than a century before the death of an emperor is again followed by civil war. And with Vespasian, as it turns out, the year has ended well.

Vespasian is unusual in the line of Roman emperors to this date in being an experienced and hard-bitten old general, non-patrician in his background and already sixty when he comes to power. He has distinguished himself in campaigns stretching back to the invasion of Britain in AD 43. Even a past threat to his career might be considered a case of critical judgement; accompanying Nero to Greece, he is so incautious as to fall asleep while the emperor is singing. He narrowly escapes severe punishment.

He is the ideal man to rebuild Roman confidence, and to replenish the treasury, by tough and sensible measures after the chaos of civil war.

The Flavian emperors: AD 69-96

Vespasian has the great advantage, on coming to power, of having two adult sons. The elder of the two, Titus, already has considerable military experience. For the first time, in almost a century since the beginning of the empire, the question of the succession need not be a pressing affair of state. In the event both sons follow Vespasian on the throne, the three of them being known (from their family name of Flavius) as the Flavian emperors.

While frugal in his own life, and unflinching in his raising of taxes, Vespasian also knows how to please the Romans. His most lavish undertaking is the building of the Flavian amphitheatre, known to history as the Colosseum.

On his accession Vespasian entrusts the important Jewish war, previously his own concern, to his son Titus. In AD 70 Titus captures and sacks Jerusalem, destroying the Temple and bearing off its treasures - including the sacred menorah, or seven-branched candelabrum, as depicted in the triumphal Arch of Titus in Rome.

Other frontier districts are forcibly pacified in a similar manner, with the result that after ten years of rule Vespasian bequeaths to his son a Roman empire in better order than at any time since the early part of the century.

In a short reign of only two years, from 79 to 81, Titus makes himself extremely popular. Part of the reason is lavish expenditure in the capital, but the same generosity is applied to two disasters which fall in this period. Pompeii and the surrounding district is buried under the ashes of Vesuvius in 79, and Rome suffers another major fire in 80. On both occasions Titus responds with prompt and effective support.

His brother Domitian, in a longer reign (81-96), leaves a less glowing reputation. One reason is an inclination towards an oriental style of divine monarchy. His effigy begins to appear among those of the gods, and he insists on being addressed as dominus et deus (master and god).

The later years of Domitian's reign are also marked by unpredictable and cruel acts which amount, by the end, to a reign of a terror. They provoke a response from commanders of the Praetorian guard in league with the emperor's wife, Domitia. In 96, having secured the compliance of a safe successor (the elderly statesman Nerva, certain to be acceptable to the senate), they arrange for the emperor's assassination.

Nerva, entering office as an elderly caretaker, has one overriding responsibility - to find a worth successor. He does so, triumphantly, in Trajan.